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Fundamentals of Physics Chapter 43 Solutions: Energy from the Nucleus

Resnick Halliday & Walker Fundamentals of Physics Volume 2 Solutions Chapter 43 ‘Energy from the Nucleus’ enables you to prepare for the class 12 Board examination as well as competitive exams like JEE and NEET. After learning this chapter, you will be ace with the topics like fission process, Bohr-Wheeler model, Neutron leakage, energy and capture problem, Thermonuclear fusion, magnetic and inertial confinement approach and identifying multiplication factor. Along with a few terms, you will also learn a few calculations based on conditions.

Resnick Halliday and Walker Fundamentals of Physics Volume 2 ‘Energy from the Nucleus’ solutions consists of 49 questions divided into six different modules. These questions are a combination of descriptive and numerical calculations. Under the calculative type of questions, you will have to calculate the height of the Coulomb barrier, the ratio of proton number density, disintegration energy, the energy released in the fission process. Additionally, you will see some statements in the question. In this, you are asked to verify it by stating the law and proving with your descriptive answers.

There isn’t any doubt that the concept of ‘Energy from the Nucleus’ is a bit difficult to understand. Therefore, Instasolv took a step forward to help you learn and understand each of the modules with easy answers and explanations. Formulas are explained clearly with the complete logic in Halliday Resnick and Walker Fundamentals of Physics Volume 2 Solutions. By going through the solutions from Insasolv, you will get the access to the clarity and interesting reasons to learn the chapter for Class 12 board exams along with competitive exams like NEET, JEE Mains and JEE Advanced.

Important Topics for Resnick Halliday & Walker Fundamentals of Physics Volume 2 Solutions Chapter 43: Energy from the Nucleus

In accordance with physics, nuclear sources provide useful energy to humans. But there is a difference between the two energy sources. We are messing with atoms of carbon and oxygen by rearranging their outer electrons when we burn wood and coal to get energy from them. By electromagnetic Coulomb force, electrons are held in atoms and nucleons are held in nuclei. To pull them out, it takes a few electron volts for electrons and a few million electron volts for nucleons. The release of energy is accompanied by a decrease in mass to the equation Q= – Δ mc2

Nuclear Fission: The basic Process

After the discovery of neutrons by James Chadwick in 1932, many physicists have researched that different radioactive elements produced when neutrons bombard various elements. But the puzzle was solved by Meitner and Otto Frisch. They suggested that with the release of energy into two equal parts, one might be barium, it can split uranium nuclei having absorbed a thermal neutron. This process was named as Fission.

  •  In a typical 235 U fission event, when the nucleus absorbs thermal neutrons, it produces a compound nucleus. That nucleus undergoes into fission and splits it into two fragments. Keep in mind that during the fission of compound nuclei, there is the conservation of the number of protons and neutrons involved in the process.
  • Those fragments then undergo a beta process. In this, the mass numbers of fragments remain unchanged whereas the atomic numbers increase by unity one step.
  • The primary fragments have too many neutrons. Thus, beta decay offers a mechanism to eject few neutrons so they can change them into protons within the nucleus.
  • The ideation of fissions lies because the total mass-energy will decrease that is ΔEben will increase. So, the fission products are more tightly bound. 

This generates Q = total final binding energy – initial binding energy.

  • By assuming that fission transforms an initial high mass nucleus to two middle mass nuclei by not changing the number of neutrons, we see that for a high mass nuclide ( A ≈ 240), the binding energy per nucleon is about 7.6 MeV/ nucleon. Similarly, for middle-class nuclides ( A ≈ 120), it is about 8.5 MeV/ nucleon
  •  Thus, the energy released by the fission of high mass nuclide to two middle mass nuclides is Q ≈  200 MeV.

The Nuclear Model

To explain the main nuclear feature, Niels Bohr and John Wheeler used the collective model of the nucleus based on the analogy between a nucleus and a charged liquid drop.

  •  Let’s say a high mass nucleus 235U absorbs a slow neutral with little kinetic energy becoming U.
  • Then the energy is transferred from mass-energy to the energy of the oscillations caused by the absorption.
  • Both the glob contains protons which are positively charged. Thus, they repel from each other.
  • With the effect of strong force protons and neutrons attract one another. They work to bind the nucleus.
  •  With the reason of distance between the globs, the force quickly decreases.
  • Therefore, the electric repulsion rips apart the nucleus if the globs move apart enough.
  • This way the energy is released when the fission decreases the mass-energy.
  • Those two fragments eject neutrons that continuously release mass-energy.

The Nuclear Reactor

Three difficulties are faced in the way of nuclear reactors.

  • The neutron leakage problem
  • The neutron energy problem
  • The neutron capture problem

One of the important nuclear reactor parameters is the multiplication factor k. It is a ratio of the number of neutrons present at the conclusion of a particular generation at the beginning of the generation.

Thermonuclear Fusion: The Basic Process

During the fusion process, when the energy is released, that process is disrupted by the Coulomb repulsion. This acts to prevent two positive charged particles from getting close enough. At that time the range of a nuclear force is short but the range of Coulomb force is long. This results in an energy barrier.

Nuclear fusion is bound to occur in the bulk matter in order to generate a particular amount of energy. It can be best attained by raising the temperature of the material until the particles have enough energy. This process is called Thermonuclear fusion. In this study, the temperature is reported in terms of kinetic energy K.

Thus, K= kT

Where K is the kinetic energy, k is the Boltzmann constant and T is the temperature.

Thermonuclear Fusion in the Sun and Other Stars

In the sun, the fusion reaction is a multistep process. Here, hydrogen is burned to form helium. The proton-proton (p-p) cycle starts with the collision of two protons to form a deuteron, simultaneously creating positron and neutrino. Under this process, protons fuse to form an alpha particle.

Controlled Thermonuclear Fusion

There are three important requirements for a successful thermonuclear fusion.

  • A high particle Density (n)
  • A high Plasma Temperature (T)
  • A long Confinement Time (τ)

Lawson’s criterion shows the successful operation of a thermonuclear reactor using the d-t reaction.

n >102s/m3

Two approaches are possible to attain the controlled thermonuclear fusion

  1. Magnetic confinement
  2. Inertial confinement

Exercise Discussions for Resnick Halliday & Walker Volume 2 Solutions Chapter 43: Energy from the Nucleus

Module 1: Nuclear Fission

Module 43-1 consists of 17 questions related to nuclear fission. Here you will have to find alpha decay events, beta decay events, Calculate disintegration energy,  find the number of atoms and energy. Percentage of volume change, surface area and electric potential energy.

Module 2: The Nuclear Reactor

Module 43-2 of Resnick Halliday and Walker Volume 2 Energy From the Nucleus Solutions has 8 questions. Here you will be asked to show the power output of a reactor. For that, you need to use the multiplication factor. Apart from that, there are questions where you will calculate effective disintegration energy.

Module 3: A Natural Nuclear Reactor

Module 43-3 involves just 4 questions of a natural nuclear reactor. Questions asking the average power level, the amount of uranium consumed would be seen.

Module 4: Thermonuclear Fusion: The basic Process

In module 43-4, you will be encountered with 5 questions. Under this module, you will have to calculate the height of Coulomb barrier, the voltage required for the collusion of deuterons, radii of the nuclei and ratio of proton number density to the number density at the average proton energy.

Module 5: Thermonuclear Fusion in the sun

Under the module 43-5, you will witness 13 questions with respect to thermonuclear fusion in the sun. the questions will demand to find Q for the fusion process, calculate the energy released, the power generated based on a few assumptions. You will be solving many comparisons in this module.

Module 6: Controlled Thermonuclear Fusion

Last module 43-6 of chapter 43 ‘Energy from the nucleus’ consists of only 2 questions. One question is about verifying Q.  In the next question, you will have to find the average fusion power.

Why Use Halliday Resnick and Walker Fundamentals of Physics Volume 2 Solutions Chapter 43: Energy from the Nucleus by Instasolv?

  • Instasolv works for your betterment. Our approach not only helps you to access the material but also makes the learning more convenient.
  • Refer to our Resnick Halliday & Walker Solutions for Fundamentals of Physics anytime and anywhere while you prepare for competitive exams like JEE along with Class 12 board exams. 
  • Instasolv is prepared in a way that allows you to understand every concept of the chapter thoroughly so that you don’t find any doubt striking in your mind while learning from it.